unit 4 – gases and atmospheric...

SCH3U: Gases and Atmospheric Chemistry

Unit 5 – Gases and Atmospheric Chemistry

The Kinetic Molecular Theory: solids, liquids, and gases are composed of particles that are continually moving and colliding with other particles. These particles may be atoms, ions, or molecules. As they move about, they collide with each other and with objects in their path. 3 types of motion that a particle can exhibit: translational (straight-line), rotational (spinning), and vibrational (back-and-forth motion of atoms within the molecule)

All moving objects have energy called kinetic energy. The faster the motion of an object, the greater its kinetic energy. The temperature of an object is a measure of the average kinetic energy of its particles. Ex: Ice as it is heated becomes liquid and eventually steam as the temperature reaches 100°C. The H2O molecules begin by vibrating, as more space becomes available, the molecules start rotating. Once they have absorbed enough energy, the translational movement is too strong for the H-bonds and the water molecule becomes steam (a gas). Explaining the Gas State Assumption: there are no attractive forces between gas molecules and the molecules move in straight lines independently of each other.


Boyle’s Law: Pressure and Volume Pressure of a gas is a force per unit area exerted by the moving molecules as they collide with objects in their path, particularly the walls of a container. The SI unit for pressure is the pascal (Pa), it represents a force of 1 N (newton) on an area of 1m2. 1 Pa = 1 N/m2 Atmospheric pressure of many gases are often more conveniently measured in kilopascals (kPa) 1 kPa = 1000 Pa = 1 kN/m2 At sea level, average atmospheric pressure is about 101 kPa. Scientists used this value as a basis to define one standard atmosphere (1 atm), or standard pressure, as exactly 101.325 kPa. For convenience, standard ambient pressure has been more recently defined as exactly 100 kPa. 25°C and a pressure of 100 kPa is known as standard ambient temperature and pressure (SATP) Evangelista Torricelli inverted a glass tube filled with mercury and placed it into a tub also containing mercury and noticed that the level of mercury changed from day to day. This device, now called a mercury barometer, was a means of mesuring atmospheric pressure. The standard pressure was defined as 760 torr or 760 mm Hg.


Sl and Non-Sl Units of Pressure

Convert SATP – 100 kPa into the corresponding values of atmospheres and millimetres of Hg. Step 1. Find the relationship between kPa and mm Hg 760 mm Hg : 101.325 kPa Step 2. Write the relationship as a fraction, with the unit you want to find as the numerator,

kPammHg325.101

760

Step 3. Multiply the given value by the conversion factor developed in Step 2. 100 kPa * 760 mm Hg ÷ 101.325 kPa = 750.06 mm Hg Statement The atmospheric pressure expressed in mm Hg is 750.06 mm Hg. Experimental data showed that mathematically that p·v = k, where k is a constant. This simple relationship was first determined by Robert Boyle in 1662. Boyle’s law states that as pressure on a gas increases, the volume of the gas decreases proportionally, provided that the temperature and amount of gas remain constant.

P1V1=P2V2


Sample: A 2.0 L party ballon at 98 kPa is taken to the top of a mountain where the pressure is 75 kPa. Assume the temperature is the same. What is the new volume of the balloon? P1 = 98 kPa P2 = 75 kPa V1 = 2.0 L V2 = ? P1V1 = P2V2 → V2 = P1V1 ÷ P2 V2 = 75 kPa x 2.0 L ÷ 98 kPa V2 = 1.53 L The volume of the ballon at the top of the mountain would be 1.53 L. Charles’s Law – Volume and Temperature Jacques Charles, more then a century after Boyle, determined a relationship between the volume and temperature of a gas by observing the hot-air balloons that were popular flying machines near 1783. Absolute zero is the lowest possible temperature and represents the extrapolated lines of temperature vs volume of gas charts. It’s value is –273°C (-273.15°C precisely) and referred to as 0 K (Kelvin). Absolute zero is the basis of another temperature scale, called the absolute or Kelvin temperature scale. To convert degrees Celsius to kelvin, simply add 273. This would make SATP 298 K and 100 kPa. Charles’s law, which states that, as the temperature of a gas increases, the volume increases proportionally, provided that the pressure and amount of gas remain constant.


Sample: A gas inside a cylinder with a movable piston is to be heated to 315°C. The volume of gas in the cylinder is 0.30 L at 25°C. What is the final volume when the temperature is 315°C? * All temperatures must be in Kelvin* 315°C = 315 + 273 = 588 K 25°C = 25 + 273 = 298 K V1 = 0.30 L V2 = ? T1 = 298 K T2 = 588 K V2 = V1 x T2 ÷ T1 V2 = 0.30 L x 588 k ÷ 298 K V2 = 0.59 L So the volume of the cylinder would be 0.59 L at the higher temperature. Pressure and Temperature Law Warnings on any aerosol can caution about the danger of the can exploding if heated. Raising the temperature increases the pressure of the gas inside until the can no longer contain the pressure and it ruptures. Mathematically, this means that as the temperature of a gas increases, the pressure increases proportionally, provided that the volume and amount of gas remain constant. Gay-Lussac's Law

Sample: A sealed storage tank contains argon gas at 18°C and a pressure of 875 kPa at night. What is the new pressure if the tank and its contents warm to 32°C during the day? 18°C = 18 + 273 = 291 K, 32°C = 32 + 273 = 305 K P1 = 875 kPa P2 = ? T1 = 291 K T2 = 305 K P2 = P1 x T2 ÷ T1 P2 = 875 kPa x 305 K ÷ 291 kPa P2 = 917.10 kPa


The Combined Gas Law It states the relationship among the volume, temperature, and pressure of any fixed amount of gas, when Boyle’s, Charles’s, and Gay-Lussac's laws are combined.

A variable that is constant can easily be eliminated from the combined gas law equation. For example, a steel cylinder with a fixed volume contains a gas at a pressure of 652 kPa and a temperature of 25°C. If the cylinder is heated to 150°C, what will be the new pressure? T1 = 25°C = 25 + 273 = 298 K T2 = 150°C = 150 + 273 = 423 K P1 = 652 kPa P2 = ? V1 = V2

P2 = P1 x T2 ÷ T1 P2 = 652 kPa X 423 K ÷ 298 K P2 = 925.49 kPa Sample: A balloon containing hydrogen gas at 20°C and a pressure of 100 kPa has a volume of 7.50 L. Calculate the volume of the balloon after it rises 10 km into the upper atmosphere, where the temperature is -36°C and the outside air pressure is 28 kPa. Assume that no hydrogen gas escapes and that balloons are free to expand so that the gas pressure within them remains equal to the air pressure outside. T1 = 20°C = 20 + 273 = 293 K T2 = -36°C = -36 + 273 = 237 K P1 = 100 kPa P2 = 28 kPa V1 = 7.50 L V2 = ? V2 = P1V1T2 ÷ T1P2 V2 = 100 kPa x 7.50 L x 237 K ÷ 293 x 28 kPa V2 = 21.67 L


The Ideal Gas Law An ideal gas is a hypothetical gas that obeys all the gas laws perfectly under all conditions; that is, it does not condense into a liquid when cooled, and graphs of its volume and temperature and of its pressure and temperature relationships are perfectly straight lines.

This is the ideal gas law, and the constant R is known as the gas constant. R= 8.13 kPa·L/mol·K Sample: What mass of neon gas should be introduced into an evacuated 0.88 L tube to produce a pressure of 90 kPa at 30°C? P = 90 kPa V = 0.88 L n = ? R = 8.13 kPa·L/mol·K T = 30°C = 30 + 273 = 303 K n = PV ÷ RT = 90 kPa x 0.88 L ÷ 8.13 kPa·L/mol·K x 303 K n = 0.03215 mol m = n x mm = 0.03215 mol x 20.18 g/mol m = 0.65 g We should introduce a mass of 0.65 g of Neon gas into the tube.


Worksheet 5.1: Gas Laws 1. Complete the following table. Show your work using appropriate conversion factors.

2. A bicycle pump contains 0.650 L of air at 101 kPa. If the pump is closed, what pressure is required to change the volume to 0.250 L? 3. A small oxygen canister contains 110 mL of oxygen gas at a pressure of 3.0 atm. This oxygen is released into a balloon with a final pressure of 2.0 atm. What is the final volume of the balloon? 4. Convert the following Celsius temperatures to kelvin:

(a) 0°C (b) 100°C (c) –30°C (d) 25°C

5. Convert the following values in kelvin to Celsius temperatures: (a) 0 K (b) 100 K (c) 300 K (d) 373 K

6. Butane lighters work very poorly outdoors in very cold weather. If 12.7 mL of butane gas is released from a lighter at 22°C, what volume would this same amount of butane occupy at –11°C? 7. An open, “empty” 2-L plastic pop container, which has an actual inside volume of 2.05 L, is removed from a refrigerator at 5°C and allowed to warm up to 21°C on a kitchen counter. What volume of air, measured at 21°C, will leave the container as it warms? 8. A closed, “empty” tank containing air at 97 kPa and 22°C survives intact in a fire. If the tank is able to withstand a maximum internal pressure of 350 kPa, what is the maximum temperature it could have reached during the fire? 9. A syringe contains 50.0 mL of a gas at a pressure of 101 kPa. The end is sealed and the plunger is pushed to compress the gas to a volume of 12.5 mL. What is the new pressure, assuming constant temperature? 10. A storage tank is designed to hold a fixed volume of butane gas at 150 kPa and 35°C. To prevent dangerous pressure buildup, the tank has a relief valve that opens at 250 kPa. At what (Celsius) temperature does the valve open? 11. A cylinder of helium gas has a volume of 1.0 L. The gas in the cylinder exerts a pressure of 800 kPa at 30°C. What volume would this gas occupy at SATP?


12. A syringe contains 50.0 mL of a gas at a pressure of 101 kPa. The end is sealed and the plunger is pushed to compress the gas to a volume of 12.5 mL. What is the new pressure, assuming constant temperature? 13. Carbon dioxide produced by yeast in bread dough causes the dough to rise, even before it is baked. During baking, the carbon dioxide gas expands. Predict the final volume of 0.10 L of carbon dioxide in bread dough that is heated from 25°C to 190°C at a constant pressure. 14. A storage tank is designed to hold a fixed volume of butane gas at 150 kPa and 35°C. To prevent dangerous pressure buildup, the tank has a relief valve that opens at 250 kPa. At what (Celsius) temperature does the valve open? 15. A balloon has a volume of 5.00 L at 20°C and 100 kPa. What is its volume at 35°C and 90 kPa? 16. A cylinder of helium gas has a volume of 1.0 L. The gas in the cylinder exerts a pressure of 800 kPa at 30°C. What volume would this gas occupy at SATP? 17. For any of the calculations in the previous questions, does the result depend on the identity of the gas? Explain briefly. 18. A 2.0-mL bubble of gas is released at the bottom of a lake where the pressure is 6.5 atm and the temperature is 10°C. What is the volume of the gas bubble when it reaches the surface, where the pressure is 0.95 atm and the temperature is 24°C? 19. List three ways of reducing the volume of gas in a shock absorber (cylinder and piston) of an automobile. 20. Under what conditions is a gas closest to the properties of an ideal gas? Why? 21. What amount of methane gas is present in a sample that has a volume of 500 mL at 35.0°C and 210 kPa? 22. What volume does 50 kg of oxygen gas occupy at a pressure of 150 kPa and a temperature of 125°C? 23. The density of a gas is the mass per unit volume of the gas in units of, for example, grams per litre. By finding the mass of one litre (assume 1.00 L) of gas, you can then calculate the density of the gas.

(a) What is the density of propane, C3H8(g), at 22°C and 96.7 kPa? (b) If the density of air at this temperature is 1.2 g/L, what happens to propane gas that may leak from a propane cylinder in a basement or from the tank of an automobile in an underground parkade? Why is this a problem?

24. Determining the molar mass of gases is an important experiment for qualitative analysis. Starting with the ideal gas law, derive a formula to calculate the molar mass, M, of a gas, given the mass and volume of the gas at a specific pressure and temperature, and that n = m / Mm.

unit 4 – gases and atmospheric...

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